A note on spectrum analysis of augmentation block Schur complement preconditioners
In this note, as a generalization of the preconditioner presented by Greif et al. (SIAM J Matrix Anal Appl 27:779–792, 2006), we consider a set of augmentation block Schur complement preconditioners for solving saddle point systems whose coefficient matrices have singular (1,1) blocks. The spectral properties of the preconditioned matrices are analyzed and an optimal preconditioner is derived.
KeywordsBlock preconditioners Saddle point systems Minimal polynomial Augmentation Nullity
AMS 2000 Subject Classifications65F10 65N20
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